We propose a psycholinguistically moti-vated version of TAG which is designed to model key properties of human sentence processing, viz., incrementality, connect-edness, and prediction. We use findings from human experiments to motivate an in-cremental grammar formalism that makes it possible to build fully connected struc-tures on a word-by-word basis. A key idea of the approach is to explicitly model the prediction of upcoming material and the subsequent verification and integration pro-cesses. We also propose a linking theory that links the predictions of our formalism to experimental data such as reading times, and illustrate how it can capture psycholin-guistic results on the processing of either... or structures and relative clauses.